System and method for fuzzy filtering images

Abstract

An invention provides a system and method for filtering pixels in an image using only fixed-point and summation operations. First, a filtering window is centered on an input pixel. Based on a difference between the intensity of the input pixel and its neighboring pixels, fuzzy filter weights are obtained. A sum of the fuzzy filter weights is used to determine a normalization factor. Then, the pixel intensities, fuzzy filter weights and the normalization factor are used to obtain an output pixel corresponding to the input pixel.

1 . A method for filtering pixels in an image, each pixel having an associated intensity, comprising the steps of: 
 centering a filtering window on an input pixel, the filtering window including the input pixel and a plurality of neighboring pixels adjacent to the input pixel;    determining a weight for each pixel in the filtering window, each weight being an integer;    summing the weights;    mapping the summed weights to a normalization factor;    multiplying the weight and the intensity of each pixel in the filtering window to obtain a product for each pixel in the filtering window;    summing the products; and    multiplying the summed products by the normalization factor to obtain an intensity of an output pixel corresponding to the input pixel.    
   
   
       2 . The method of  claim 1 , further comprising: 
 basing the weights on an exponential function.    
   
   
       3 . The method of  claim 2 , further comprising: 
 approximating the exponential function by a look-up table.    
   
   
       4 . The method of  claim 2 , further comprising: 
 approximating linearly the exponential function.    
   
   
       5 . The method of  claim 3 , in which the look-up table includes the weights indexed by integers, and further comprising: 
 measuring, for each pixel in the filtering window, a difference between the intensity of the pixel and the intensity of the input pixel; and    selecting the weight by mapping the difference to the index of the weight in the look-up table.    
   
   
       6 . The method of  claim 5 , in which the look-up table has a full size S FULL =2 M , where M is the number of bits used to represent the intensity of the input pixel.  
   
   
       7 . The method of  claim 5 , in which the look-up table has a reduced size where weights less than a predetermined threshold are defined as zero.  
   
   
       8 . The method of  claim 4 , further comprising: 
 measuring, for each pixel in the filtering window, a difference between the intensity of the pixel and the intensity of the input pixel; and    generating the weight by evaluating the linear approximation according to the difference.    
   
   
       9 . The method of  claim 2 , further comprising: 
 controlling the exponential function with a spread parameter.    
   
   
       10 . The method of  claim 9 , in which the spread parameter is twenty.  
   
   
       11 . The method of  claim 9 , in which the spread parameter is variable according to each pixel in the filtering window.  
   
   
       12 . The method of  claim 1 , in which a size of the filtering window is three by three pixels.  
   
   
       13 . The method of  claim 1 , in which a size of the filtering window is variable.  
   
   
       14 . The method of  claim 1 , in which the weights are integers.  
   
   
       15 . The method of  claim 2 , in which the exponential function represents a fuzzy filter.  
   
   
       16 . A system for filtering pixels in an image, each pixel having an associated intensity, comprising: 
 means for centering a filtering window on an input pixel, the filtering window including the input pixel and a plurality of neighboring pixels adjacent to the input pixel;    means for determining a weight for each pixel in the filtering window, each weight being an integer;    a first adder for summing the weights;    means for mapping the summed weights to a normalization factor;    a first multiplier for multiplying the weight and the intensity of each pixel in the filtering window to obtain a product for each pixel in the filtering window;    a second adder for summing the products; and    a second multiplier for multiplying the summed products by the normalization factor to obtain an intensity of an output pixel corresponding to the input pixel.